I've never used it. Does it work like Sheen does?

Yes, in that it applies a damage increasing buff when you cast a spell.

Note:
Does not stack with Lich bane
Does not stack with Sheen (I did some science on this, and I think it may actually overwrite Triforce with Sheen if you have both. Which is even more reason not to try and stack them)
Works on next physical hit.

Its much bether have no coold down, so every spell followed by a atack ll do trinity dmg

Yes, Trinity Force has a Super-Unique* Passive that behaves identically to Sheen's, only with a 150% damage increase on the next hit instead of 100%. In addition, it gives the components of all three component "swords" (Sheen, Phage, Zeal) in an increased amount: HP, MP, Attack Damage, AP, Move Speed, Attack Speed, Crit Chance, Slow on Hit.

*It is Super-Unique in that it does not stack with the Unique Passives of Sheen or Lich Bane. Boots are the only other Unique Passive to not stack with different item's passives of the same type.

Also @Max, there is no way to have "No Cooldown", as Cooldown reduction caps at -40%. Additionally, Sheen/Lichbane/Triforce all have a cooldown of 3 seconds on their ability, meaning even if you are spamming spells faster than that somehow (Like Hate Spike on Eve), you don't get multiple procs of Sheen/Lichbane/Triforce in a row.

trinity force don t have cooldown

in other words, attackspeed and tri force on eve is great.

edited for incorrectness. apologies.

Lichbane is affected by AP, so likewise.. stacking AP will make the proc hit harder on the autoattack after an ability is used.

Both procs are affects by Crit Chance, so that also helps.

Sheen/Trinity only work with base damage